Both Iran and the United States have blamed each other for the failure to reach agreement to limit Tehran's uranium enrichment in exchange for an easing of Western sanctions.

But despite the accusations, there are hopes the next round of talks in Switzerland could bring the parties—Iran on one side and on the other the six world powers, which include the five permanent U.N. Security Council members and Germany—closer to a peaceful resolution of the decade-long nuclear standoff with the Islamic Republic.

The countries worry that Tehran is trying to assemble an atomic weapons arsenal, a charge Iran denies, insisting its nuclear program is solely for peaceful energy production and medical research.

Iran refuses to completely give up uranium enrichment—but the level of enrichment has become a key aspect of the ongoing Geneva talks.

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Halting the 20 percent enrichment—a level Iran has acknowledged and which is several steps away from weapons-grade material—is a key goal of Western envoys.

Zarif, the foreign minister, said there was no chance of success at the next round if the West ignores Iran's demand.

"Any agreement that does not recognize the rights of the Iranian people and does not respect these rights, has no chance," Zarif said.

Echoing Zarif's hopes, Ayatollah Kazem Seddighi, an advisor to Iran's Supreme Leader Ayatollah Ali Khamenei, said during the Friday prayers sermon in Tehran there was still an opportunity for a deal.

"There are still grounds (for agreement) if everybody is tolerant," Sedighi said. "We expect the West to use this opportunity."

Pressure has been building within the U.S. Congress to toughen economic sanctions America already has in place against Iran. Samantha Power, the U.S. ambassador to the United Nations, said Friday that more time is needed, without new sanctions, to pursue a deal.

"We have to test this regime." Power told "CBS This Morning." She said one key obstacle is the "generations of suspicion" between the two countries.

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